Q. 4 - Calculus

Question

In Exercises 3–8, let A, B, C, D, ... , Z be points in $R^3$. Simplify the given quantity.

$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}$

Step-by-Step Solution

Answer

$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}=\overrightarrow{AD}$

Step 1: Given

$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}$

Step 2: Simplify

From the law of vector addition,

$$\begin{gathered} \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}=\left(\overrightarrow{AB}+\overrightarrow{BC}\right)+\overrightarrow{CD} \\ =\overrightarrow{AC}+\overrightarrow{CD} \\ =\overrightarrow{AD} \end{gathered}$$